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The Einstein equations
express the metric evolution
in terms of the matter sources.
With the
form of the scalar metric and stress energy tensor given
in Eqns. (36) and (39), the ``Poisson''
equations become

| |
(56) |

where the corresponding matter evolution is
given by covariant conservation of the stress energy tensor
,
for the fluid part, where . These equations
express energy
and momentum density conservation respectively.
They remain true for each fluid individually in the absence
of momentum exchange. Note
that for the photons
, and . Massless
neutrinos obey Eqn. (60) without the Thomson
coupling term.
Momentum exchange
between the baryons and photons due to Thomson scattering
follows by noting that for a given velocity perturbation
the momentum density ratio between the two fluids is

| |
(57) |

A comparison with photon Euler equation (60) (with
, *m*=0) gives the
baryon equations as
For a seed source, the conservation equations become
since the metric fluctuations produce higher order terms.

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*Wayne Hu*

*9/9/1997*